The table below gives the U.S. consumer price index (CPI) for selected years from 2012 and projected

Question:

The table below gives the U.S. consumer price index (CPI) for selected years from 2012 and projected to 2050. With the reference year as 2012, a 2020 CPI = 120.56 means goods and services that cost $100.00 in 2012 are expected to cost $120.56 in 2020.
(a) Find the quadratic function that is the best fit for the data, with x as the number of years past 2010 and y as the CPI in dollars. Report the model as y = f(x) with three significant digit coefficients.
(b) Use the data to find the average rate of change of the CPI from 2012 to 2020.
(c) Find the derivative of the reported model found in part (a).
(d) Find the instantaneous rate of change of the CPI for the year 2020.
(e) Use the rate of change from part (d) to predict the CPI for 2022.